Gluon fragmentation into P-wave heavy quarkonium.

The fragmentation functions for gluons to split into P-wave heavy quarkonium states are calculated to leading order in the QCD coupling constant. Long-distance effects are factored into two nonperturbative parameters: the derivative of the radial wavefunction at the origin and a second parameter related to the probability for a heavy-quark-antiquark pair that is produced in a color-octet S-wave state to form a color-singlet P-wave bound state. The fragmentation probabilities for a high transverse momentum gluon to split into the P-wave charmonium states χc0, χc1, and χc2 are estimated to be 0.4×10−4, 1.8×10−4, and 2.4×10−4, respectively. This fragmentation process may account for a significant fraction of the rate for the inclusive production of χcJ at large transverse momentum in pp̄ colliders. on leave from Dept. of Physics and Astronomy, Northwestern University, Evanston, IL 60208 Heavy quarkonium plays an important role in high energy collider physics, because these states can probe physical processes at short distances of order 1/mQ, where mQ is the heavy quark mass. Of particular importance experimentally are the 1 S-wave states of charmonium and bottomonium, which have very clean signatures through their leptonic decay modes, and the J P-wave states with J = 0, 1, 2, which can also be observed through their radiative transitions into the 1 states. In most previous studies of the direct production of heavy quarkonium [1], the dominant production mechanisms were assumed to be given by the Feynman diagrams that were lowest order in the QCD coupling constant αs. It has recently been pointed out that the dominant mechanism for heavy quarkonium production at large transverse momentum pT is fragmentation, the production of a high energy parton with even larger transverse momentum which subsequently decays into the quarkonium state plus other partons [2]. While this mechanism is often of higher order in the QCD coupling constant αs than conventional mechanisms, it is enhanced at large transverse momentum by powers of pT/mQ, and thus dominates at sufficiently large pT . The fragmentation of a parton i into any hadron H is described by a universal fragmentation function Di→H(z, μ), where z is the longitudinal momentum fraction of the hadron relative to the parton and μ is a factorization scale of order pT [3]. If the fragmentation function is known at some initial momentum scale μ0, then it can be determined at larger momentum scales μ by solving the Altarelli-Parisi evolution equations which sum up the leading logarithms of μ/μ0. In Ref. [2], it was shown that in the case of heavy quarkonium, the fragmentation function D(z,mQ) at an initial scale of order mQ can be calculated using perturbative QCD. The initial fragmentation functions for gluons to split into S-wave states of heavy quarkonium were calculated to leading order in αs [2]. The fragmentation functions for heavy quarks to split into S-wave states have also been calculated to leading order [4, 5, 6], and these calculations have recently been extended to the P-wave states [7]. In this paper, we calculate the fragmentation functions for gluons to split into the P-wave states to leading order in αs. For the sake of clarity, we describe the calculation in terms of the lowest P-wave states of the charmonium system: the J = J states χcJ , with J = 0, 1, 2, and the 1 state hc. Our results apply equally well to the higher P-wave states of charmonium, as well as to the P-wave states of the bottomonium system. While a